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Homework Help: Isomorphic groups

  1. Aug 17, 2011 #1
    1. The problem statement, all variables and given/known data

    For any positive integern, let U(n) be the group of all positive integers less than n and relatively prime to n, under multiplication modulo n. Show the the Groups U(5) and u(10) are isomorphic
    2. Relevant equations



    3. The attempt at a solution

    any 2 cyclic groups of the same size have to be isomorphic.
    For the answer to this problem should i do out a caley table for both groups to show they are cyclic? is this enough along with my statement? i guess what im saying is...does the question ask me to prove that 2 cyclic groups of the same size are isomorphic?
     
  2. jcsd
  3. Aug 17, 2011 #2
    Re: Isomorphic

    No, a Cayley table would be overkill!! (although it would work).

    I suggest you first work out what U(5) and U(10) is explicitely. Try to prove that they have the same order.
    Then try to find a cyclic element in both groups.
     
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